The Gerundive: अनीयर् तव्यत् (& य)

The gerundive in Sanskrit grammar is also called the prescriptive passive participle, and indicates something that should be done, or is worth doing. It has the force of the विधि लिङ् (optative mode) and is formed by adding the suffixes य, तव्य and अनीय​ to the root of the verbal action. 

Examples:

ज्ञा >>ज्ञेय to be known
पा >>पेय to be drunk
भू >>भव्य​ to be

भू >>भवितव्य to be, to happen
कृ >>कर्तव्य to be done
पठ् >>पठितव्य​ to be read/studied

कृ >>करणीय worth doing, to be done
पठ् >>पठनीय to be read 
पूज्  >>पूजनीय​ worthy of being worshiped

The meaning remains pretty much the same, though one root can have many gerundives:
कृ >>कृत्य, कार्य, कर्तव्य, करणीय

In terms of usage in a sentence, like the कर्मणि and भावे  prayoga, the कर्तृ or the 'doer' of the action​ is expressed in तृतीया or the instrumental case (though often it is found in षष्ठी or the genitive case e.g. सः मे मान्यः =he is respected by me.) However the participle/gerundive itself will be formed in two ways - depending on whether the verbal root is सकर्मक (transitive) अकर्मक (intransitive). Let is see how*.

सकर्मक (transitive)

Notice that the gerundive agrees with the कर्मन् (object) in gender, number and case. And that like the कर्मणि (passive) prayoga, the object is in the nominative, or प्रथमा vibhakti.

न केनपि ब्राह्मण: हन्तव्यः
A brahmin should not be killed by anyone
नारी अपि न कदापि हन्तव्या
A woman too is never to be killed

रामेण राज्यम् करणीयम्
RAma should rule the kingdom (राज्यम् nominative, neuter प्रथमा नपुंसक​)
मया पाठ: पठनीय​:
I should study this lesson

मया ग्रन्थः पठितव्य:
I should study this text (lit. this text is worthy of being studied by me)


अकर्मक (intransitive)

The gerundive of the intransitive is equivalent to भावे prayoga. So the कर्तृ doer is in तृतीया or the instrumental case or in षष्ठी or the genitive case. However since there is no कर्मन् (object) with which it has to agree (see above), it is nominative, singular, neuter प्रथमा एक नपुंसकलिन्ङ्ग.

अत्र मया स्थातव्यम्

Lit. It is to be stayed here by me = I ought to stay here. 
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Note:
भू is used idiomatically sometimes in the sense of probability or likelihood. In which case, the subject and predicate will be in the same case:

तेन राज्ञा भवितव्यम्
(he must be/become king)
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*The formation is different for आत्मने पद​ verbs, but we'll deal with them in a separate write-up.
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